Affine and Projective Geometry
In this chapter we shall introduce two different (but closely related) geometrical languages. The first of these, the language of affine geometry, is the one which appeals most closely to our intuitive ideas of geometry. In this language the subspaces of a vector space of dimensions 0, 1 and 2 are called “points”, “lines” and “planes”, respectively. But we cannot limit these words to describe only subspaces: otherwise V would have only one point, namely the zero subspace, and every line and plane in V would contain this point. Our intuition suggests that we introduce the concept of “translated” subspace.
KeywordsProjective Plane Vector Space Versus Projective Geometry Division Ring Projective Dimension
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- Except where we state the contrary, all vector spaces considered in the remainder of this book are assumed to be finite dimensional.Google Scholar